Into a unit square you drop two needles (having negligible width) of lengthL. (0 < L < sqrt(2)). Consider the probabilityp( L ) that they will intersect. A moment's thought reveals that the probability approaches zero as Lapproaches zero. p( L )is a strictly increasing function and approaches a limit as L approaches sqrt (2).
What is the maximum value of p( L )?
Clue
Spoiler
This is as much a logic puzzle as a mathematical one.
Inspired by BMAD's Pickup Sticks puzzle, I ask the following related question.
Into a unit square you drop two needles (having negligible width) of length L. (0 < L < sqrt(2)). Consider the probability p( L ) that they will intersect. A moment's thought reveals that the probability approaches zero as L approaches zero. p( L ) is a strictly increasing function and approaches a limit as L approaches sqrt (2).
What is the maximum value of p( L )?
Clue
This is as much a logic puzzle as a mathematical one.
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